For an angle satisfying it is given that .

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

For an angle θ\theta satisfying π2<θ<π\dfrac{\pi}{2}<\theta<\pi it is given that sin⁡θ=35\sin \theta=\dfrac{3}{5}. (i) Determine cos⁡θ\cos \theta. (ii) Find the exact value of cos⁡3θ\cos 3\theta. (iii) Hence calculate sin⁡3θ\sin 3\theta and tan⁡3θ\tan 3\theta. Express each answer in simplest fractional form.

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